RPA puzzle in C(12) weak decay processes

We explain the origin of the difficulties that appear in a straightforward application of the QRPA in C(12), and we demonstrate that it is imperative to use the projected QRPA (PQRPA). Satisfactory results, not only for the weak processes among the ground states of the triad B(12),C(12),N(12), but also for the inclusive ones are obtained. We sketch as well a new formalism for the neutrino-nucleus interaction that furnishes very simple final formulae for the muon capture rate and neutrino induced cross sections.Comment: 14 pages in LaTex, changes are included in the text, to appear in PL

A formalism for weak interactions in nuclei

The neutrino-nucleus cross-section and the muon capture rate are discussed within a simple formalism which facilitates the nuclear structure calculations. The corresponding formulae only depend on four types of nuclear matrix elements, which are currently used in the nuclear beta decay. We have also considered the non-locality effects arising from the velocity-dependent terms in the hadronic current. We show that for both observables in 12C the higher order relativistic corrections are of the order of ∼ 4% only, and therefore do not play a significant role.Facultad de Ciencias Exacta

Violation of the Ikeda sum rule and the self-consistency in the renormalized quasiparticle random phase approximation and the nuclear double-beta decay

The effect of the inclusion of ground state correlations into the QRPA equation of motion for the two-neutrino double beta ($\beta\beta_{2\nu}$) decay is carefully analyzed. The resulting model, called renormalized QRPA (RQRPA), does not collapse near the physical value of the nuclear force strength in the particle-particle channel, as happens with the ordinary QRPA. Still, the $\beta\beta_{2\nu}$ transition amplitude is only slightly less sensitive on this parameter in the RQRPA than that in the plain QRPA. It is argued that this fact reveals once more that the characteristic behaviour of the $\beta\beta_{2\nu}$ transition amplitude within the QRPA is not an artifact of the model, but a consequence of the partial restoration of the spin-isospin $SU(4)$ symmetry. It is shown that the price paid for bypassing the collapse in the RQRPA is the violation of the Ikeda sum rule.Comment: 16 pages, latex, 3 postscript figure

Neutrino and antineutrino cross sections in 12C

We extend our formalism of weak interaction processes, obtaining new expressions for the transition rates, which greatly facilitate numerical calculations, of neutrino (ν) and antineutrino (ν)-nucleus reactions and the muon capture. We have done a thorough study of exclusive (ground state) properties of 12B and 12N within the Projected Quasiparticle Random Phase Approximation (PQRPA). Good agreement with experimental data is achieved in this way. The inclusive ν/ν-nucleus reactions 12C(ν, e-)12N and 12C(ν, e+)12B are calculated within both the PQRPA, and the Relativistic QRPA (RQRPA). It is found that the magnitudes of the resulting cross-sections: i) are close to the sum-rule limit at low energy, but significantly smaller than this limit at high energies both for ν and ν, ii) steadily increase when the size of the configuration space is augmented, and particulary for ν/ν energies > 200 MeV, and iii) converge for sufficiently large configuration spaces and final state angular momenta.Facultad de Ciencias Exacta

Quasiparticle-rotor model description of carbon isotopes

In this work we perform quasiparticle-rotor coupling model calculations within the usual BCS and the projected BCS for the carbon isotopes 15C, 17C and 19C using 13C as the building block. Owing to the pairing correlation, we find that 13C as well as the cores of the other isotopes, namely 14C, 16C and 18C acquire strong and varied deformations. The deformation parameter is large and negative for 12C, very small (or zero) for 14C and large and positive for 16C and 18C. This finding casts a doubt about the purity of the supposed simple one-neutron halo nature of 19C.Instituto de Física La PlataFacultad de Ciencias Astronómicas y Geofísica

One-nucleon-induced nonmesonic hypernuclear decay in laboratory coordinates

We present a formalism for the computation of one-nucleon-induced nonmesonic weak hypernuclear decay rates in laboratory coordinates, within an independent-particle shell model framework, with a view to its generalization to the case of two-nucleon-induced transitions.Fil: Galeão, A. P.. Universidade Estadual Paulista Julio de Mesquita Filho. Instituto de Física Teórica; BrasilFil: Barbero, Cesar Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico La Plata. Instituto de Física La Plata; Argentina. Universidad Nacional de la Plata. Facultad de Ciencias Exactas; ArgentinaFil: de Conti, C.. Universidade Estadual Paulista Julio de Mesquita Filho. Campus Experimental de Itapeva; BrasilFil: Krmpotic, Francisco. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico La Plata. Instituto de Física La Plata; Argentina. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentin